Effective Action for the Scalar Field Theory with Higher Vertices

TL;DR

This paper introduces a novel recursion relation to compute the effective action's 1PI diagrams, successfully deriving the four-loop effective action for bosonic theories with higher-than-four-point vertices.

Contribution

It presents a new recursive method for calculating the effective action's diagrams in theories with complex higher-order vertices.

Findings

Derived a recursion relation for 1PI diagrams.

Graphical representation of four-loop effective action.

Applicable to bosonic theories with higher vertices.

Abstract

We derive a new kind of recursion relation to obtain the one-particle-irreducible (1PI) Feynman diagrams for the effective action. By using this method, we have obtained the graphical representation of the four-loop effective action in case of the general bosonic field theory which have vertices higher than the four-point vertex.